Car X is 40 miles west of Car Y. Both cars are travelling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?
Let Y's rate = y.
Since X's rate is 50% faster -- in other words, 1.5 times Y's rate -- X's rate = (3/2)y.
The CATCH-UP rate is the DIFFERENCE between the two rates:
(3/2)y - y = (1/2)y.
To catch up to Y, 40 miles must be traveled.
The time taken is 8/3 hours (the equivalent of 2 hours, 40 minutes).
Since d = r*t, we get:
40 = (1/2)y * 8/3
120 = 4y
y = 30.
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